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The Joule – Brayton cylce was first proposed by George Brayton. A simple gas – turbine system consists of a compressor, a combustion chamber and a gas turbine, which is shown in the following figure:

As shown in this figure, gas at ambient condition (①) is drawn into the compressor and flows out of it with increased temperature and pressure (②). The compressed gas flows then into the combustion chamber, where the fuel is burnt at constant pressure. The heat released from the fuel leads to increase further the temperature of gas (③). This resulting high temperature gas then enters into the turbine, expands to the atmospheric pressure and leaves the turbine (④). During this expansion process, power is produced by turbine.

This Joule – Brayton process can be idealized by the four internally reversible processes (shown in T-s and p-v diagram):

1→2: isentropic compression (in compressor)

2→3: heat supplied to compressed air due to combustion of fuel at constant pressure

3→4: isentropic expansion (in turbine)

4→1: heat rejection at constant pressure

We notice that all these four processes are steady and also assume that working gas is perfect gas and the changes in kinetic and potential energies can be neglected, then we can calculate the thermal efficiency:

Heat transferred to compressed gas (2→3): q_{1}=c_{p}∙(T_{3} – T_{2})

Heat rejected from gas (4→1): q_{2}=c_{p}∙(T_{1} – T_{4})

What’s more, since 1→2 and 3→4 are isentropic processes, we can obtain additional the following relation:

Therefore the thermal efficiency relation yields:

This equation implies that the thermal efficiency increases with the pressure ration (p_{2}/p_{1}) and the specific heat ratio κ.

Now we will determine, under which condition we can get the maximal power produced by turbine:

w=q_{1}+q_{2}= c_{p}∙(T_{3} – T_{2})+ c_{p}∙(T_{1} – T_{4}) with T_{4}=(T_{3}∙T_{1})/T_{2}

If we compare with T_{4}∙T_{2}=(T_{3}∙T_{1}), we notice that we obtain the maximal produced power, if T_{4}=T_{2}!